The non-mystery was explained at length in a 1998 New Times story by Tony Ortega. What follows is the Cliffs Notes explanation:

There were two events that night: a "vee pattern" of lights that flew across the state north-to-south, which crossed Phoenix around 8:30 p.m., and a second set of nine lights that seemed to hover over Phoenix, before apparently disappearing.

As for the first event, a man in Scottsdale looking through a large Dobsonian telescope identified the lights as being attached to planes.

From Ortega's story:

It was plain to see, [Mitch] Stanley says. Under magnification, Stanley could clearly see that each light split into pairs, one each on the tips of squarish wings. Even under the telescope's power, the planes appeared small, indicating that they were flying high. Stanley says he followed the planes for about a minute, then turned his telescope to more interesting objects.

"They were planes. There's no way I could have mistaken that," he says.

The more widely seen, and talked-about lights were the ones hovering around 10 p.m. From Ortega:

Within days, Tucson Weekly broke the news that the Maryland Air National Guard, in Arizona for winter training, had a squad of A-10 fighters over the gunnery range that night, and they had dropped flares. An Arizona National Guard public information officer, Captain Eileen Bienz, had determined that the flares had been dropped at 10 p.m. over the North Tac range 30 miles southwest of Phoenix, at an unusually high altitude: 15,000 feet.

The "disappearance" was actually the lights dropping behind the Sierra Estrella mountain range. Channel 12 filmed a similar dropping of flares by military planes, which Ortega reported as looking "remarkably like the 10 p.m. lights of March 13."

An ASU astronomy professor, a physicist, and other scientists have reviewed the evidence, and found the explanation perfectly plausible. In fact, you can still find that physicist's complete report online.

As for the "vee," which wasn't talked about or disputed as much as the hovering lights, it never was disclosed who was flying those planes. According to Ortega's report, Luke Air Force radar operators said there was nothing unusual on the radar, and "a formation of five planes--traveling at high altitude above Sky Harbor's and outside of Luke's restricted air spaces--would not have been considered unusual."

Nobody bothered to request the radar information from the Federal Aviation Administration within two weeks, when such records were routinely deleted, so it'll never be known exactly where those planes came from.

However, the claim by UFO hunters was that this was some miles-long UFO (obviously alien) didn't pan out. Some people thought all the lights were part of one craft, but an analysis of the videotape made it clear that they were moving together in a formation, but they were independent of one another.